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Unsupervised Classification of Aerial Images Based on the Otsu’s Method 175
2.2.2 Unsupervised classification strategy by within-class and between-classes
spectral variances
There are three steps in the proposed classification strategy. First, the assignment process,
that consists in assigning one of the possible classes to each pixel. Second, the codification of
each cluster, which is identified by a label. Finally, a regrouping process so that very similar
classes are merged into one.
2.2.2.1 Assignment process
Given a pixel i located at (x, y) in the original RGB image. Its three spectral components in
this space are obtained, namely R(x, y) = ir, G(x, y) = ig and B(x, y) = ib.
As already mentioned, the thresholding methods split the histogram into two regions. As
there are three spectral components, six sub-regions are obtained. If necessary, successive
thresholding can be applied to each spectral channel. The second thresholding produces
three partitions per channel. If a third thresholding is applied, four regions per component
are obtained and so on. Therefore, assuming that eventually the number of thresholds per
channel is M, there will be tR1, tR2, … tRM , thresholds for channel R, and in the same way, tG1,
tG2, …, tGM for component G, and tB1, tB2, …, tBM, for component B. Based on this, each pixel i
can be coded as is according to its spectral components by Equation (10):
0 if i t
1 if t i t
i
s 2 if t i t
M if is tsM
s s1
s1 s s2
s2 s s3
where s denotes the spectral component, i.e., s = R, G or B, and tsi are the consecutive
thresholds.
For example, it is known that in the RGB colour space values are in the range [0, 255]. So,
considering the spectral component R with two thresholds, tR1 = 120 and tR2 = 199, a pixel
will be coded as 0, 1, or 2, if its spectral value R is smaller than 120, between 120 and 199, or
greater than 199, respectively.
2.2.2.2 Cluster labelling
Once the whole image has been coded, the next step is the labelling of the existing classes. If
M thresholds haven been obtained, there are n = M + 1 histogram partitions per channel,
and therefore the number of possible combinations is nd, where d is the number of spectral
components, i.e., d = 3 in the RGB colour space. This number of combinations represents the
number of classes. Each cluster is identified by its label. Every pixel is assigned its
corresponding label according to Equation (11). So, given the pixel i ≡ (x, y) with codes , ı, and ı, its label will be given by P as follows:
2
i R G B
(10)
p ni ni i
(11)
2.2.2.3 Merging process
Let Ck be the number of clusters obtained by the classification procedure, where k identifies
a class between 1 and nd, each class containing Nk pixels of the original image. It could be